Deck 3: Numbers in the Real World

Question 1

Answer the question.

A)The second tape measure gives a more precise reading but the first tape measure gives a more accurate reading.
B)The first tape measure gives a more precise reading and also a more accurate reading.
C)The first tape measure gives a more precise reading but the second tape measure gives a more accurate reading.
D)The second tape measure gives a more precise reading and also a more accurate reading.

Answer 1

C

Question 2

Answer the question.
In 2000 your salary increased by 15% . In 2001 you received a 15% pay cut. After the two changes, how does your salary compare to your original salary?

A)It is higher.
B)Cannot be determined from the information given
C)It is unchanged.
D)It is lower.

Answer 2

D

Question 3

Answer the question.
Of those who applied to the college, 50% were accepted and of those accepted, 10% enrolled. What percentage of those who applied, enrolled?

Answer 3

B

Question 4

Answer the question.
Between 1990 and 2000, the population of Emeryville grew from 20,000 to 25,000 while the population of Sun City grew from 100,000 to 110,000. Which of the statements below is correct?

A)Emeryville had greater absolute growth in population, and also greater relative growth.
B)Emeryville had greater absolute growth in population, but Sun City had greater relative growth.
C)Sun City had greater absolute growth in population, and also greater relative growth.
D)Sun City had greater absolute growth in population, but Emeryville had greater relative growth.

Question 5

Answer the question.
A teacher gives the same math exam to two different classes. The second class has more students than the first. The mean score for the first class is 70% and the mean score for the second class is
90%. What can you say about the mean score for both classes combined?

A)It is equal to 80%.
B)It may be higher or lower than 80%, this cannot be determined from the information given.
C)It is higher than 80%.
D)It is lower than 80%.

Question 6

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described.
The total amount of money spent each year on food by Americans.

A)Ten billion dollars
B)One trillion dollars
C)Thirty trillion dollars
D)One hundred billion dollars

Question 7

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described.
The weight of a grain of rice.

A)0.0006 ounces
B)0.000001 ounces
C)0.006 ounces
D)0.01 ounces

Question 8

Solve the problem.
During the sale the price of the sofa was discounted by 15%. Determine which of the statement's below is true.

A)The sale price of the sofa is 85% less than the regular price.
B)The sale price of the sofa is 85% of the regular price.
C)The sale price of the sofa is 15% of the regular price.
D)The regular price of the sofa is 101% of the sale price.

Question 9

Answer the question.
Suppose that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 92% of those who don't have the disease. Suppose also that
The incidence of the disease is 1%. If a person tests positive for the disease, what can you say about
Their chance of having the disease?

A)It is about 50%
B)It is 95%
C)It is quite low
D)It is very high

Question 10

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described.
The total number of steps an adult would take in walking from New York to San Francisco.

A)One billion
B)One hundred million
C)One million
D)Ten million

Question 11

Answer the question.
If your salary is 25% higher than mine, then how does my salary compare to your salary?

A)My salary is 25% less than yours.
B)My salary is 20% less than yours.
C)My salary is 75% of yours.
D)My salary is 125% of yours.

Question 12

Answer the question.
Which of the statements below suggests an appropriate level of precision?

A)The population of sperm whales worldwide is 817,213
B)The population of sperm whales worldwide is 800,000.
C)The population of sperm whales worldwide is 817,210.
D)The population of sperm whales worldwide is 817,200.

Question 13

Answer the question.
A researcher looks at the percentage of people having high blood pressure amongst those who exercise regularly and amongst those who do not exercise regularly.
She selects 300 people under 40, of whom 100 exercise regularly and 200 do not. Among those who
Exercise regularly the rate of high blood pressure is 10% and among those who do not exercise
Regularly it is 15%.
She then selects 300 people over 40, of whom 200 exercise regularly and 100 do not. Among those
Who exercise regularly the rate of high blood pressure is 30% and among those who do not exercise
Regularly it is 35%.
However when she combines both age groups she finds that among those who exercise regularly
The rate of high blood pressure is 23.3% and among those who do not exercise regularly it is 21.7%.
Explain how the apparent inconsistency in these results came about.

A)Mistakes must have been made in measuring blood pressures.
B)Those that do not exercise regularly must be receiving some other treatment to lower their blood pressure.
C)The people in the "regular exercise" group probably started exercising because they have high blood pressure.
D)The group that exercises regularly contains a greater proportion of older people than the group that does not exercise regularly. So when the age groups are combined, the "regular
Exercise" group has a higher rate of high blood pressure.

Question 14

Answer the question.

Question 15

Answer the question.
Two candidates for governor of a state differ in their accounts of the state's economy during the incumbent's term. The incumbent claims that during his four-year term the economy has
Improved, citing a rise in the median household income from $33,000 to $34,500. The challenger
Claims that the economy has declined, citing that the buying power of families in the state has
Declined during the four years. Which of the following best explains how both candidates can be
Right?

A)Only those in the middle income group saw their incomes rise, those with lower and higher incomes actually saw their incomes decline during the incumbent's term.
B)Though the median household income increased, prices increased by a greater percent, meaning that in real terms the median income actually decreased.
C)The incumbent is referring to the state economy, while the challenger is referring to the national economy.
D)It is not possible for both candidates to be right; one of them is obviously lying.

Question 16

Answer the question.
Which of the statements below suggests an appropriate level of precision?

Question 17

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described.
The total number of gallons of gasoline that will be used by American drivers in a year.

A)One trillion
B)Ten trillion
C)One hundred billion
D)Ten billion

Question 18

Solve the problem.
The area of Jose's apartment is 45% more than the area of Alan's apartment. Determine which of the statement's below is true.

A)The area of Jose's apartment is 145% more than the area of Alan's apartment.
B)The area of Jose's apartment is 45% of the area of Alan's apartment.
C)The area of Jose's apartment is 145% of the area of Alan's apartment.
D)The area of Alan's apartment is 45% less than the area of Jose's apartment.

Question 19

Answer the question.
Which of the statements below suggests an appropriate level of precision?

A)Worldwide there will be 133.147 million births next year.
B)Worldwide there will be 133,147,763 births next year.
C)Worldwide there will be 100 million births next year. [to the nearest one hundred million]
D)Worldwide there will be 133 million births next year.

Question 20

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described.
The thickness of a compact disc.

A)0.05 inches
B)0.1 inches
C)0.01 inches
D)0.005 inches

Question 21

Answer the question.
The average annual precipitation in Tewinville is 70 inches. In 2000, a particularly wet year, the precipitation was 140 inches. Which of the following statements are correct? More than one
Statement may be correct.
A: In 2000, the precipitation was 200% of normal.
B: In 2000, the precipitation was 100% of normal.
C: In 2000, the precipitation was 200% above normal.
D: In 2000, the precipitation was 100% above normal.

A)A and C
B)B and C
C)A and D
D)B and D

Question 22

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described.
The total number of cups of coffee drunk last year by Europeans.

A)Ten billion
B)Ten trillion
C)Two trillion
D)Two hundred billion

Question 23

Answer the question.
Which of the statements below suggests an appropriate level of precision?

A)According to his bathroom scales, Enrique's weight is 190 lb [to the nearest ten pounds]
B)According to his bathroom scales, Enrique's weight is 194.113 lb.
C)According to his bathroom scales, Enrique's weight is 194.1134 lb.
D)According to his bathroom scales, Enrique's weight is 194 lb.

Question 24

Answer the question.
Suppose that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 90% of those who don't have the disease. Suppose also that
The incidence of the disease is 1%. If a person tests positive for the disease, what is the chance that
They have the disease? Find the exact percentage.

A)13.4%
B)10%
C)95%
D)8.8%

Question 25

Answer the question.
Which of the statements below suggests an appropriate level of precision?

A)8314 people have enrolled for the college for next year.
B)8000 people have enrolled for the college for next year. [Number given to the nearest thousand]
C)8300 people have enrolled for the college for next year. [Number given to the nearest hundred]
D)8314.1 people have enrolled for the college for next year.

Question 26

Answer the question.
In the 1980s, the population of Pleasanton decreased by 10%. In the 1990s, its population increased by 30%. How does the population of Pleasanton at the end of the 1990s compare with its
Population in 1980?

A)It is 17% higher.
B)It is 23% higher.
C)It is 40% higher.
D)It is 20% higher.

Question 27

Solve the problem.
The value of her house today is 400% more than when she bought it. Determine which of the statement's below is true.

A)The value of her house today is 5 times what it was when she bought it.
B)The value of her house today is 400% of the value when she bought it.
C)The value of her house today is 4 times what it was when she bought it.
D)The value of her house today is 500% more than when she bought it.

Question 28

Solve the problem.
Cathy scored 7 times as much as Helen on the test. Determine which of the statement's below is true.

A)Cathy's score was 700% of Helen's score.
B)Helen's score was 600% less than Cathy's score.
C)Cathy's score was 600% of Helen's score.
D)Cathy's score was 700% more than Helen's score.

Question 29

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described.
The total number of breaths taken in his lifetime by a man who lives to be 80.

A)Three hundred million
B)Fifty million
C)Ten billion
D)Three billion

Question 30

Solve the problem.
John is 6 times as heavy as his dog. Determine which of the statement's below is true.

A)John weighs 600% more than his dog.
B)John weight is 500% of his dog's weight.
C)John's dog weighs 500% less than John.
D)John weighs 500% more than his dog.

Question 31

Answer the question.
In 2000 a company increased its workforce by 60%. In 2001 it decreased its workforce by 60%. How does the size of its workforce at the end of 2001 compare with the size of the workforce at the
Beginning of 2000?

A)It is unchanged.
B)It is 6% lower.
C)It is 36% higher.
D)It is 36% lower.

Question 32

Solve the problem.
Allison weighs 29% less than she did one year ago. Determine which of the statement's below is true.

A)Allison's current weight is 29% of her weight one year ago.
B)Allison's current weight is 71% of her weight one year ago.
C)Allison's weight one year ago is 129% of her current weight .
D)Allison's current weight is 129% of her weight one year ago.

Question 33

Answer the question.
A researcher looks at the percentage of people having high blood pressure amongst those who exercise regularly and amongst those who do not exercise regularly.
She selects 300 people under 40, of whom 200 exercise regularly and 100 do not. Among those who
Exercise regularly the rate of high blood pressure is 10% and among those who do not exercise
Regularly it is 15%.
She then selects 300 people over 40, of whom 100 exercise regularly and 200 do not. Among those
Who exercise regularly the rate of high blood pressure is 30% and among those who do not exercise
Regularly it is 35%.
However when she combines both age groups she finds that among those who exercise regularly
The rate of high blood pressure is 23.3% and among those who do not exercise regularly it is 21.6%.
Explain the apparent inconsistency in these results.

A)Among those who exercise regularly, younger people have a lower rate of high blood pressure, and among those who do not exercise regularly younger people have a lower rate of
High blood pressure. But looking at both groups combined, young people have a higher rate
Of high blood pressure.
B)In spite of exercising, people get older.
C)Within each age group the percentage with high blood pressure is lower amongst those who exercise, but when the age groups are combined, the percentage with high blood pressure is
Higher amongst those who exercise.
D)Within the under-40 age group the percentage with high blood pressure is lower amongst those who exercise, but within the over-40 age group, the percentage with high blood
Pressure is higher amongst those who exercise.

Question 34

Answer the question.
Which of the statements below suggests an appropriate level of precision?

A)The number of people at the demonstration was 120,000.
B)The number of people at the demonstration was 122,600.
C)The number of people at the demonstration was 100,000 [to the nearest one hundred thousand].
D)The number of people at the demonstration was 122,615.

Question 35

Answer the question.
In 2000, the balance on Martin's credit card increased by 50%. In 2001, the balance increased by 10%. How does the balance at the end of 2001 compare to the balance at the beginning of 2000?

A)It is 65% higher.
B)It is 100% higher.
C)It is 55% higher.
D)It is 60% higher.

Question 36

Answer the question.
In Slackville, the unemployment rate was 20% last year and this year it is 24%. Which of the following statements is correct?

A)In absolute terms, the unemployment rate this year is 4 percentage points higher than last year and in relative terms it is 16.7% higher.
B)In absolute terms, the unemployment rate this year is 20 percentage points higher than last year and in relative terms it is 4% higher.
C)In absolute terms, the unemployment rate this year is 4 percentage points higher than last year and in relative terms it is 20% higher.
D)In absolute terms, the unemployment rate this year is 4 percentage points higher than last year and in relative terms it is 4% higher.

Question 37

Answer the question.
Which of the statements below suggests an appropriate level of precision?

A)Every day I drive a distance of 75.134 miles to work.
B)Every day I drive a distance of 76 miles to work.
C)Every day I drive a distance of 80 miles to work. [to the nearest 10 miles]
D)Every day I drive a distance of 75.1341 miles to work.

Question 38

Answer the question.
Suppose that of the total amount collected in taxes by the U.S. government, 25% of it comes from families with incomes greater than $200,000.
If taxes are increased by 5% across the board, which of the following statements will be true?

A)5% of the additional revenue will come from each income group.
B)The total amount collected from families with incomes greater than $200,000 will increase by 25%.
C)A family with an income greater than $200,000 will have to pay 25% more in taxes.
D)25% of the additional revenue collected by the government will come from families with incomes greater than $200,000.

Question 39

Solve the problem.
The retail cost of a computer is 22% more than its wholesale cost. Determine which of the statement's below is true.

A)The retail cost of the computer is 122% more than the wholesale price.
B)The retail cost of the computer is 122% of the wholesale price.
C)The wholesale cost of the computer is 78% of the retail price.
D)The retail cost of the computer is 22% of the wholesale price.

Question 40

Answer the question.
Any test for a disease has a certain rate of false positives (percentage of those who don't have the disease who test positive)and a certain rate of false negatives (percentage of those who do have the
Disease who test negative).
You would like to determine the chance that a person has the disease given that they have tested
Positive for the disease. Which of the following will you need to know?

A)The rate of false positives, the incidence of the disease
B)The rate of false positives, the rate of false negatives, the incidence of the disease
C)The rate of false positives, the rate of false negatives, the incidence of the disease, the number of people being tested
D)The rate of false positives, the rate of false negatives

Question 41

Use the Consumer Price Index below to answer the question.
In 1992, Sue rented out her apartment for $760 per month. In 2000 she charged $800 per
month.
Convert the 1992 price to 2000 dollars. In real terms, how does the actual price in 2000
compare to the price in 1992? Explain your reasoning.

Question 42

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror.
According to police reports, attendance at the last three anti-war rallies was 45,000, 60,000,
and 22,300 respectively.

Question 43

Use the Consumer Price Index below to answer the question.
The table below shows the federal hourly minimum wage in various years. What was the relative change in the minimum wage from 1990 to 1997? How does this
compare to the overall rate of inflation as measured by the CPI? In which of those two
years was the purchasing power of the minimum wage higher?

Question 44

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror.
You use a tape measure to measure people's heights.

Question 45

Write the word or phrase that best completes each statement or answers the question.For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror.
An agency wishes to determine the number of unemployed people in a town. They
conduct a mini-census by delivering a survey to every household in the town, asking for
information about household members. The information is entered into a computer.

Question 46

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror.
You use your wrist watch to time your friends running 200 meters.

Question 47

Give an appropriate response.
The tables below show the results of a study examining the incidence of breast cancer
among women who exercise regularly and those who do not.
The 425 women in the study were split into two age groups, those under 40 and those 40
or older. For each age group, determine the percentage of women having breast cancer among
those exercise regularly and among those who do not exercise regularly. If the two age
groups are combined, what percentage have breast cancer among those who exercise
regularly and among those who do not exercise regularly?
Explain the apparent inconsistency in these results, and how the design of the study
brought about the inconsistency.

Question 48

Give an appropriate response.
The following table shows the deaths due to the same disease in two cities. Compute the
death rates in each city for those with health insurance, those without health insurance,
and all residents. Explain the apparent inconsistency in these results.

Question 49

Use the Consumer Price Index below to answer the question.
The table below shows the federal hourly minimum wage in various years. Complete the
table by converting each minimum wage from actual dollars to 2001 dollars. In which year
was the purchasing power of the minimum wage the highest?

Question 50

Carry out the indicated operation and give your answer with the specified number of significant digits.

Question 51

Give an appropriate response.
Due to poor sales, a company eliminated a number of jobs. Twenty-five percent of the 300
men in full-time positions lost their jobs, while 20% of the 300 women in full-time
positions lost their jobs. 80% of the 150 men in part-time positions lost their jobs, and 75%
of the 600 women in part-time positions lost their jobs. Explain the apparent inconsistency
in these results.

Question 52

Use the Consumer Price Index below to answer the question.
Between 1990 and 2000, a college raised its annual tuition fees from $4690 to $6630. Find
the relative change in the fees over that period and compare it to the overall rate of
inflation as measured by the CPI. Were the tuition increases in line with inflation?

Question 53

Use the Consumer Price Index below to answer the question.
In 1995, the price of gasoline was 120.5 cents per gallon. In 2000 it was 155.0 cents per
gallon. Find the relative change in the price of gasoline over that period and compare it to
the overall rate of inflation as measured by the CPI. In real terms, was gasoline more
expensive in 1995 or 2000?

Question 54

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror.
Round to the nearest hundred: 482.106

A)480
B)500
C)400

Question 55

Decide whether the statement is believable, given the precision with which it is stated.
Last year, the company made $199.2 in profits.

A)Believable
B)Not believable at that precision

Question 56

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror.
The average weight of 100 college-age women, found by asking them their weight during
interviews conducted at their college.

Question 57

Use the Consumer Price Index below to answer the question.
Which of the following is greater? Explain why this makes sense.

Question 58

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror.
You estimate the speed of other cars by pulling up behind a car, driving at the same speed,
and looking at your speedometer.

Question 59

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematicerror.
The average income of 100 people is calculated by using the incomes which they reported
on credit card applications. These incomes are entered onto a computer and a statistical
package is used to calculate the average income.

Question 60

Give an appropriate response.
The table shows the results of a study examining the effectiveness of home schooling as
compared to traditional schooling. The same reading test is given to all students regardless
of grade. For each age grade, determine the percentage passing the test amongst those schooled at
home and among those with traditional schooling. If the two age groups are combined,
what percentage pass the test amongst those schooled at home and among those with
traditional schooling?
Explain the apparent inconsistency in these results, and how the design of the study
brought about the inconsistency.

Question 61

Answer the question.

Question 62

Write the number in scientific notation.

Question 63

Use the Consumer Price Index below to answer the question.
Suppose you needed $56,000 to maintain a particular standard of living in 2000. How much would you have needed in 1990 to maintain the same standard of living?

A)$74,000
B)$44,000
C)$43,000
D)$41,000

Question 64

Restate the fact as indicated.
The speed of light is approximately 5,866,000,000,000 miles per year. Express this speed in miles per second.

A)4,460,000 miles per second
B)3100.2 miles per second
C)186,009.6 miles per second
D)11,160,578.4 miles per second

Question 65

Solve the problem.
The table below shows the number of people testing positive for a certain disease amongst those who do have the disease and amongst those who don't. Use the table to answer the question. What percentage of those that don't have the disease tested negative?

A)98.6%
B)90.1%
C)99.8%
D)88.9%

Question 66

Round to the indicated place value.

Question 67

Solve the problem.
The percentage of registered voters who voted in this election was 54%, up 20% from the last election. What was the percentage that voted at the last election?

A)45%
B)64.8%
C)43.2%
D)34%

Question 68

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits.
Find your speed by dividing the distance you traveled, 259 kilometers, by the time, 2.1 hours.

A)123.3 kilometers per hour
B)123 kilometers per hour
C)100 kilometers per hour
D)120 kilometers per hour

Question 69

Determine ratio of A to B. Round as indicated.

Question 70

Answer the question.
Suppose you are constructing a scale model solar system using a scale ratio of 1 to 100 billion. In your scale model what will be the distance from Neptune to the Sun (in meters)? The distance from
Neptune to the Sun is 4497 million km.

A)0.4497 m
B)4.497 m
C)44.97 m
D)0.04497 m

Question 71

Solve the problem.
Suppose the current cost of gasoline is $3.28 per gallon. Find the current price index using the 1995 price as the reference value. In 1995, the cost of gasoline was 120.5 cents per gallon.

A)36.7
B)2.7
C)272.2
D)207.5

Question 72

Write the number in scientific notation.

Question 73

Two measurements are given. Find the absolute difference and then find the relative difference as a percentage. Assumethat the first quantity is the compared value and the second quantity is the reference value. Round answers to the nearesttenth if necessary.
In a certain country, the life expectancy for men is 70.2 years while the life expectancy for women is 76.6 years.

A)Absolute difference: -6.4 years
B)Absolute difference: -6.4 years Relative difference: -8.4% Relative difference: -0.8%
C)Absolute difference: 6.4 years
D)Absolute difference: -6.4 years Relative difference: 9.1% Relative difference: -9.1%

Question 74

Determine ratio of A to B. Round as indicated.
A = 64.9 is the average number of points scored in a college basketball game. B = 49.5 is the average number of points scored in a high school basketball game. (Round to the nearest hundredth when
Necessary.)

A)13.11
B)0.76
C)0.13
D)1.31

Question 75

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits.
A city has a deficit of $31.4 million. How much is this per person if the population of the city is 263,300?

A)$100 per person
B)$119 per person
C)$120 per person
D)$119.3 per person

Question 76

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits.
You have covered 72.6 miles of a 1600 mile journey. How much further do you have to go?

A)1527.4 miles
B)1500 miles
C)1530 miles
D)1527 miles

Question 77

Use scientific notation to perform the following operations. Leave your answer in scientific notation.

Question 78

Find the absolute and relative errors.
The length of the room is 12 feet but you measure it to be 12 feet and 5 inches.

A)absolute error: -5 inches
B)absolute error: 5 inches relative error: -3.5% relative error: 3.4%
C)absolute error: 5 inches
D)absolute error: 5 inches relative error: 3.5% relative error: 4.2%

Question 79

Solve the problem.
Brand X copier advertises that its copiers run 16% longer between service calls than its competitor. If Brand X copiers run 55,300 copies between services, how many copies would the competitor run?

A)46,452 copies
B)47,672 copies
C)64,148 copies
D)30,054 copies

Question 80

Answer the question.
Find the scale ratio for a map if 4 centimeters on the map represents 10 kilometers on the ground.

A)1 : 250,000
B)1 : 2500
C)1 : 25,000
D)1 : 1,000,000